Method of determination of fluid influx profile and near-wellbore space parameters

ABSTRACT

Method for determination of a fluid influx profile and near-wellbore area parameters comprises measuring a first bottomhole pressure and operating a well at a constant production rate. After changing the production rate a second bottomhole pressure is measured together with a fluid influx temperature for each productive layer. Relative production rates and skin factors of the productive layers are calculated from measured fluid influx temperatures and measured first and second bottomhole pressures.

FIELD OF THE DISCLOSURE

The invention relates to the area of geophysical studies of oil and gas wells, particularly, to the determination of the fluid influx profile and multi-layered reservoir near-wellbore area space parameters.

BACKGROUND OF THE DISCLOSURE

A method to determine relative production rates of the productive layers using quasi-steady flux temperature values measured along the wellbore is described, e.g. in: {hacek over (C)}eremenskij G.A. Prikladnaja geotermija, Nedra, 1977 p. 181. Disadvantages of the method include low accuracy of the layers relative flow rate determination resulting from the assumption of the Joule-Thomson effect constant value for different layers. In effect, it depends on the formation pressure and specific layers pressure values.

SUMMARY OF THE DISCLOSURE

The technical result of the invention is an increased accuracy of the wellbore parameters (influx profile, values of skin factors for different productive layers) determination.

The method for the determination of a fluid influx profile and near-wellbore area parameters comprises the following steps. A bottomhole pressure is measured. The production rate is changed after a long-term operation of the well at a constant production rate during a time sufficient to provide a minimum influence of the production time on the rate of the subsequent change of the temperature of the fluids flowing from the production layers into the wellbore. The bottomhole pressure and the temperature of a fluid influx for each layer are measured. The graphs of the dependence of the temperature measured as a function of time and the derivative of this temperature by the logarithm of the time elapsed after the production rate change are plotted. Time moments at which the temperature derivatives become steady are determined and the influx temperature changes corresponding to these time moments are also determined. Relative flow rates and skin factors of the layers are calculated using the values obtained.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows the influence of the production time on the temperature change rate after the production rate change;

FIG. 2 shows the change of the temperature derivative of the fluids flowing from different productive layers by the logarithm of the time elapsed after the production rate change and times t_(d1) and t_(d2) are marked after which this value becomes steady (these values are used to calculate the layers relative flow rates);

FIG. 3 shows the dependencies of the influx temperature derivative vs. time and the determination of the influx temperature changes ΔT_(d1) and ΔT_(d2) is shown (by the times t_(d1) and t_(d2)) used to calculate the layers skin factors for the two-layer wellbore model; and

FIG. 4 shows the dependency of the bottomhole pressure vs. time elapsed after the production rate change (for the example in question).

DETAILED DESCRIPTION

The method for the measurements processing claimed in the subject disclosure is based on a simplified model of heat- and mass-transfer processes in the productive layer and wellbore. Let us consider the results of the model application for the processing of the measurement results of the temperature T_(in) ⁽¹⁾(t) of fluids flowing into the wellbore from two productive layers.

In the approximation of the productive layers pressure fast stabilization the change rate of the temperature of the fluid flowing into the wellbore after the production rate has been changed is described by the equation:

$\begin{matrix} {{\frac{T_{in}}{t} = {\frac{ɛ_{0}}{2 \cdot \left( {s + \theta} \right)} \cdot \left\lbrack {{\frac{P_{e} - P_{1}}{f\left( {t,t_{d\; 1}} \right)} \cdot \frac{1}{\left( {{\delta_{12} \cdot t_{p}} + t_{2} + t} \right)}} + {\frac{P_{1} - P_{2}}{f\left( {t,t_{d}} \right)} \cdot \frac{1}{\left( {t_{2} + t} \right)}}} \right\rbrack}},} & (1) \end{matrix}$

where P_(e) is a layer pressure, P₁ and P₂—the bottomhole pressure before and after the production rate change, s—a layer skin factor, θ=ln(r_(e)/ r_(w)), r_(e)—drain radius, r_(w)—a wellbore radius, t—the time counted from the moment of production rate change, t_(p)—production time at the bottomhole pressure of

$\begin{matrix} {P_{1},{\delta_{12} = \frac{P_{e} - P_{1}}{P_{e} - P_{2}}},{{f\left( {t,t_{d}} \right)} = \left\{ {{\begin{matrix} K & {t \leq t_{d}} \\ 1 & {{t_{d} < t},} \end{matrix}K} = {\frac{k_{d}}{k} = \left\lbrack {1 + \frac{s}{\theta_{d}}} \right\rbrack^{- 1}}} \right.}} & (2) \end{matrix}$

—a relative permeability of the bottom-hole zone, θ_(d)=ln(r_(d)/r_(w)), r_(d)—bottom-hole zone radius, t_(d1)=t₁·D and t_(d2)=t₂·D—certain characteristic heat-exchange times in layer 1 and layer 2, D=(r_(d)/r_(w))²−1—non-dimensional dimensional parameter characterizing the size of the near-wellbore area,

${t_{1,2} = \frac{\pi \cdot r_{w}^{2}}{\chi \cdot q_{1,2}}},{q_{1,2} = {\frac{Q_{1,2}}{h} = {\frac{2{\pi \cdot k}}{\mu} \cdot \frac{\left( {P_{e} - P_{1,2}} \right)}{s + \theta}}}}$

—specific volumetric production rates before (index 1) and after (index 2) the change in the production rate, Q_(1,2), h and k—volumetric production rates, thickness and permeability of the layer,

${\chi = \frac{c_{f} \cdot \rho_{f}}{\rho_{r} \cdot c_{r}}},{{\rho_{r}c_{r}} = {{{\varphi \cdot \rho_{f}}c_{f}} + {{\left( {1 - \varphi} \right) \cdot \rho_{m}}c_{m}}}},$

φ a layer porosity, ρ_(f)c_(f)—volumetric heat capacity of the fluid, ρ_(m)c_(m)—volumetric heat capacity of the rock matrix, μ—fluid viscosity. r_(d)—external radius of the near-wellbore zone with the permeability and fluid influx profile changed as compared with the properties of the layer far away from the wellbore (to be determined by a set of factors, like perforation holes properties, permeability distribution in the affected zone around the wellbore and drilling incompleteness).

According to Equation (1) at a relatively long production time t_(p) before the production rate is changed its influence on the temperature change dynamics tends towards zero. Let us evaluate this influence. For the order of magnitude χ≈0.7, r_(w)≈0.1 m, and for r_(d)=0.3 m q=100 [m³/day]/3 m≈4·10⁻⁴ m³/s we have: t₂≈0.03 hours, t_(d)=0.25 hours. If the measurement time t is t≈2÷3 hours (i.e. t>>t₂,t_(d) and f(t, t_(d))=1) it is possible to evaluate what relative error is introduced into the derivative (1) value by the finite time of the production before the measurements:

$\begin{matrix} {{\frac{1}{{\overset{.}{T}}_{in}} \cdot {\Delta \left( {\overset{.}{T}}_{in} \right)}} = {\frac{P_{e} - P_{1}}{P_{1} - P_{2}} \cdot \frac{1}{1 + \frac{t_{p}}{t}}}} & (3) \end{matrix}$

FIG. 1 shows the results of calculations by Equation (3) for P_(e)=100 Bar, P₁=50 Bar, P₂=40 Bar and t_(p)=5, 10 and 30 days. From the Figure we can see, for example, that if the time of production at a constant production rate was 10 or more days, then within t=3 hours after the change in the production rate the influence of t_(p) value on the influx temperature change rate will not exceed 6%. It is essential that the increase in the measurement time t results in the proportional increase in the required production time at the constant production rate before the measurements, so that the error value introduced by the value t_(p) in the value of the derivative (1) could be maintained unchanged.

Then it is assumed that the production time t_(p) is long enough and Equation (1) may be written as:

$\begin{matrix} {\frac{T_{in}}{t} \approx {\frac{ɛ_{0} \cdot \left( {P_{1} - P_{2}} \right)}{2 \cdot \left( {s + \theta} \right)} \cdot \frac{1}{f\left( {t,t_{d}} \right)} \cdot \frac{1}{t}}} & (4) \end{matrix}$

From Equation (4) it is seen that at a sufficient long time t>t_(d), where

$\begin{matrix} {t_{d} = \frac{\pi \cdot r_{w}^{2} \cdot D}{\chi \cdot q_{2}}} & (5) \end{matrix}$

The temperature change rate as function of time is described as a simple proportion:

$\frac{T_{in}}{{\ln}\; t} = {{const}.}$

Numerical modeling of the heat- and mass-exchange processes in the productive layers and production wellbore shows that the moment t=t_(d) may be singled out at the graph of

$\frac{T_{in}}{{\ln}\; t}$

vs. time as the beginning of the logarithmic derivative constant value section.

If we assume that the dimensions of the bottomhole areas in different layers are approximately equal (D₁≈D₂), then using times t_(d) ⁽¹⁾ and t_(d) ⁽²⁾, found for two different layers their relative production rates may be found (6):

$Y = \frac{q_{2}h_{2}}{{q_{1}h_{1}} + {q_{2}h_{2}}}$ or $Y = {\left( {1 + \frac{q_{1} \cdot h_{1}}{q_{2} \cdot h_{2}}} \right)^{- 1} = \left( {1 + {\frac{h_{1}}{t_{d}^{(1)}} \cdot \frac{t_{d}^{(2)}}{h_{2}}}} \right)^{- 1}}$

In general relative production rates of the second, third etc. layers is calculated using equations:

$\begin{matrix} {{{Y_{2} = {\frac{q_{2}h_{2}}{{q_{1}h_{1}} + {q_{2}h_{2}}} = \left\lbrack {1 + {\left( \frac{h_{1}}{t_{d,1}} \right) \cdot \frac{t_{d,2}}{h_{2}}}} \right\rbrack^{- 1}}},{Y_{3} = {\frac{q_{3}h_{3}}{{q_{1}h_{1}} + {q_{2}h_{2}} + {q_{3}h_{3}}} = \left\lbrack {1 + {\left( {\frac{h_{1}}{t_{d,1}} + \frac{h_{2}}{t_{d,2}}} \right) \cdot \frac{t_{d,3}}{h_{3}}}} \right\rbrack^{- 1}}},\begin{matrix} {Y_{4} = \frac{q_{4}h_{4}}{{q_{1}h_{1}} + {q_{2}h_{2}} + {q_{3}h_{3}} + {q_{4}h_{4}}}} \\ {{= \left\lbrack {1 + {\left( {\frac{h_{1}}{t_{d,1}} + \frac{h_{2}}{t_{d,2}} + \frac{h_{3}}{t_{d,3}}} \right) \cdot \frac{t_{d,4}}{h_{4}}}} \right\rbrack^{- 1}},} \end{matrix}}{{etc}.}} & (6) \end{matrix}$

Equation (1) is obtained for the cylindrically symmetrical flow in the layer and a bottomhole area (with the bottomhole area permeability of k_(d)≠k), which has an external radius r_(d). The temperature distribution nature in the bottomhole area is different from the temperature distribution away from the wellbore. After the production rate has been changed this temperature distribution is carried over into the well by the fluid flow which results in the fact that the nature of T_(in)(t) dependence at low times (after the production rate change) differs from T_(in)(t) dependence observed at long (t>t_(d)) time values. From Equation (7) it is seen that with the accuracy to χ coefficient the volume of the fluid produced required for the transition to the new nature of the dependence of the incoming fluid temperature T_(in)(t) vs, time is determined by the volume of the bottomhole area:

$\begin{matrix} {{t_{d} \cdot q_{2}} = {\frac{1}{\chi} \cdot \pi \cdot \left( {r_{d}^{2} - r_{w}^{2}} \right)}} & (7) \end{matrix}$

In case of perforated wellbore there always is a “bottomhole” area (regardless of the permeabilities distribution) in which the temperature distribution nature is different from the temperature distribution in the layer away from the wellbore. This is the area where the fluid flow is not symmetrical and the size of this area depends on the perforation tunnels length (L_(p)):

$\begin{matrix} {D_{p} \approx {\left( \frac{r_{w} + L_{p}}{r_{w}} \right)^{2} - 1.}} & (8) \end{matrix}$

If we assume that the lengths of perforation tunnels in different productive layers are approximately equal (D_(p1)≈D_(p2)), then relative production rates of the layers are also determined by Equation (6). Equation (8) may be updated by introducing a numerical coefficient of about 1.5-2.0, the value of which may be determined from the comparison with the numerical calculations or field data.

To determine the layer skin factor s temperature difference ΔT_(d) of the fluid flowing into the wellbore during the time between the production rate change and t_(d): time.

$\begin{matrix} {{\Delta \; T_{d}} = {\int_{0}^{t_{d}}{\frac{T_{in}}{t} \cdot \ {{t}.}}}} & (9) \end{matrix}$

Using Equation (4) we find:

$\begin{matrix} {{{\Delta \; T_{d}} = {c \cdot ɛ_{0} \cdot \left( {P_{1} - P_{2}} \right) \cdot \frac{s + \theta_{d}}{s + \theta}}},} & (10) \end{matrix}$

where ΔT_(d) is the change of the influx temperature by the time t=t_(d), (P₁−P₂)—steady-state difference between the old and the new bottomhole pressure which is achieved in the wellbore several hours after the wellbore production rate has been changed. Whereas Equation (4) does not consider the influence of the end layer pressure field tuning rate, Equation (10) includes non-dimensional coefficient c (approximately equal to one) the value of which is updated by comparing with the numerical modeling results.

According to (10), skin factor s value is calculated using equations

$\begin{matrix} {{s = \frac{{\psi \cdot \theta} - \theta_{d}}{1 - \psi}}{{{where}\mspace{14mu} \psi} = \frac{\Delta \; T_{d}}{c \cdot ɛ_{0} \cdot \left( {P_{1} - P_{2}} \right)}}} & (11) \end{matrix}$

Therefore the determination of the influx profile and productive layers skin factors includes the following steps:

1. During a long time (from 5 to 30 days depending on the planned duration and measurement accuracy requirements) the well is operated at a constant production rate.

2. The wellbore production rate is changed, the bottomhole pressure and wellbore fluid temperature T₀(t) in the influx bottom area as well as the temperature values under and over the productive layers in question are measured.

3. Derivatives from the influx temperatures dT_(in) ⁽¹⁾/dlnt are calculated and relevant curves are built

4. From these curves values t_(d) ^((i)) are found as time moments starting from which derivatives dT_(in(i))/dlnt become steady and using Equations (6) relative layer flow rates are calculated.

5. From curves T_(in) ^((i))(t) values of ΔT_(d) ^((i)) temperatures changes by t_(d) ^((i)) time moments and from Equation (11) layers skin factors are found.

The temperature of fluids flowing into the wellbore from productive layers may be measured using, for example, the apparatus described in WO 96/23957. The possibility of the determination of the influx profile and productive layers skin factors using the method claimed was checked on synthetic examples prepared by using a numerical simulator of the producing wellbore which simulates unsteady pressure field in the wellbore-layers system, non-isothermal flow of the fluids being compressed in a non-uniform porous medium, mixture of the flows in the wellbore and wellbore-layer heat exchange etc.

FIG. 2-4 shows the results of the calculation for the following two-layer model:

k₁=100 mD, s₁=0.5, h₁=4 m

k₂=500 mD, s₂=7, h₂=6 m

The production time at a production rate of Q₁=300 m³/day is t_(p)=2000 hours; Q2=400 m³/day. From FIG. 4 it is seen than in the case in question the wellbore pressure continues to change considerably even after 24 hours. FIG. 2 provides curves of the influx temperature T_(in,1) and T_(in,2) derivative from the logarithm of time elapsed after the wellbore flow rate change. From the Figure we can see that derivatives dT/dint stabilize? Respectively, at t_(d) ⁽¹⁾=0.5 hours and t_(d) ⁽²⁾=0.3 hours. Using these values we find relative production rate of the upper layer 0.72 which is close to the true value (0.77). From the curve of influx temperature as function of time (FIG. 3) using these value we find ΔT_(d) ⁽¹⁾=0.064 K, ΔT_(d) ⁽²⁾=0.152 K. In case of the layers skin factors calculation using Equation (11) by the obtained values of ΔT_(d) ⁽¹⁾ and ΔT_(d) ⁽²⁾, the calculated values of skin factors at c=1.1 differ from the true values of skin factors by less than 20%. 

1. A method for the determination of a fluid influx profile and near-wellbore area parameters comprising: measuring a bottomhole pressure, operating a well at a constant production rate during a time sufficient to provide a minimum influence of a production time on a rate of a subsequent change of a temperature of the fluids flowing from production layers into a wellbore, changing the production rate, measuring the bottomhole pressure, measuring the temperature of a fluid influx for each layer, plotting a graph of a dependence of the temperature measured as a function of time and a derivative of this temperature by a logarithm of a time elapsed after the production rate change, determining time moments at which the temperature derivatives become steady, determining the influx temperature changes corresponding to these time moments, and calculating relative flow rates and skin factors of the layers using values obtained. 